This actually isn't telepathy. Hearing train of thought is described as telepathy. To since or to feel one another is typical connection which is actually a common thing between animals and their close human counterparts. This is seen in relationships like that dealing with familiars or spirit guides or manifested totems, a sense of presence is often perceived there.

Humans often forms what we call bonds between one another, which are using what you describe as links of energy. For instance a mother who has a feeling that her daughter is sad or unhappy during the day at school.

There are various and simplistic methods to go about creating bonds with both humans and animals as well as plants, an example would be a sister tree. This being one of the more easier methods another could be naturally occurring again like that between a mother and her daughter. You have others with more ritualistic like tendencies such as blood bonding where blood may shared or shed between one another.